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Why is angular momentum conserved in a satellite?

1 Answer
Mar 8, 2018

Answer:

The principle of conservation of momentum, both linear (also known as translational) and angular, is a universal principle of Physics.

Explanation:

Angular momentum, #L#, is defined, in mathematical terms as

#L = I*omega#

Take the time derivative of that

#(dL)/dt = I*(domega)/dt#

We give the term "torque" to #I*(domega)/dt# and we give torque the variable name #tau#.
We give #(domega)/dt# the variable name #alpha#.

Expanding that last equation with the variable names #alpha and tau#

#(dL)/dt = I*(domega)/dt = I*alpha = tau# ... Equation1

The equation #tau = I*alpha# is the angular equivalent of #F = m*a# which Newton made famous in Newton's 2nd Law.

#tau, I, and alpha# are the angular equivalents of #F, m, and a# respectively.

If there are no external torques acting on a body, #tau = 0#, and that there is no angular acceleration follows. That is shown in the repeat of Equation 1 below.

#(dL)/dt = I*(domega)/dt = I*alpha = 0#

Therefore #(dL)/dt = 0#. And therefore, the angular momentum is constant if #tau = 0#.

Therefore, we have Conservation of Angular Momentum .

I hope this helps,
Steve